Welcome to the community!
And congrats on your little Conure baby, I love the Black-Capped Conures, so cute...And I'm glad that you ended-up being the people who got to take Yoshi home, and not anyone who would reject a parrot because their tail-feathers had fallen out or been pulled out, etc...LOL, their feathers do grow back-in!!! Birds actually have the ability to "Drop" their tail-feathers, all of them at one time, if they are scared or if they get them stuck in something, etc. It's a survival thing that they all are able to do, because often predators grab a hold of birds by their tail-feathers because they are easy to get a hold of, they're sticking out and they are away from their "weapon" (their beak!), so when a predator does grab onto their tail-feathers or if they get their tail-feathers stuck in/under something, they can purposely just "Drop" them all at once and go about their business, lol...Doesn't hurt them or cause the any pain at all, and they will all start growing back-in fully pretty directly after they "Drop" them...So if Yoshi came from a pet shop, someone probably tried to grab him when he didn't want to be grabbed, or maybe he got lose in the store and they were chasing him, etc., and Yoshi said "No way, check this out!!!" and then dropped his tail! So it's completely normal, and good for you for being the one to have the pleasure of adding him to your family!
I don't know how old Yoshi is now, but Green Cheeks/Black Cappeds usually go through their first molt, which is the HUGE molt, the biggest one they ever go through, between 6 months-old and a little over a year-old (about the same time they go through puberty)...I don't know what color-changes, if any, that Black-Capped Conures go through during their first molt, but I'm sure they do go through some color changes, most birds do...So when he's all done with his first molt, you'll probably see some color changes to his feathers, along with his beautiful tail-feathers growing all back-in normally...
Don't ever hesitate to ask any questions you have, no matter what they are...There's no such thing as a "stupid question", nor is there any such thing as "worrying too much" when it comes to birds...Especially if you think that they might be sick, you definitely want to be very pro-active about that...I don't know if you know this already or not, but all birds/parrots possess a natural, innate survival-instinct to hide any and all outward signs and symptoms of illness and/or pain for as long as they possibly can...So by the time we as people first notice that our birds/parrots might be sick or injured/in-pain, they have most-likely already been sick or injured for a long period of time, usually for months, sometimes for over a year, and because of this it's often too late to do anything at all to save them...
So because of this, it's extremely important that you find either a Certified Avian Vet or an Avian Specialist Vet ASAP, BEFORE Yoshi ever gets sick or injured, and you take him for a full "Wellness Exam", which you need to continue to take him for at least once yearly, if not every 6 months...A yearly Wellness-Exam should consist of a full visual and physical exam by the CAV, along with them collecting a Fecal sample (it's best that you collect his first-morning's poop the day of his appointment, put it in a plastic container or baggie, and put it in the fridge until it's time to leave for the appointment, then take it with you)...Your CAV should do basic Microscopy and a Gram-Stain on the Fecal sample right there in the office, and he should also send it out to the outside-lab they use for a "Culture and Sensitivity"...This is to rule-out that Yoshi has any Bacterial, Fungal/Yeast, or Protozoan infections, as well as confirming that he has enough normal, healthy Bacteria throughout his GI Tract, which is very, very important in birds...And then Yoshi should also have routine, "baseline" Blood-Work done also during his yearly Wellness-Exams, where they check for infection, anemia, nutritional deficiencies, and most-importantly for birds, their Liver and Kidney function and health...And you definitely want to find ONLY a Certified Avian Vet or Avian Specialist Vet, no "Exotics Vets" who treat any and all types of animals, or any General Vets...CAV's have extra education and training in just Avian Medicine, where "Exotics" Vets and General Vets do not...And the yearly Wellness-Exams that include Blood-Work and Fecal testing are the very best way to ensure that your bird is not hiding any serious medical/health issues...If you need help finding CAV's in your area, there is a great search tool here...
Lastly, what is Yoshi's regular, daily diet? That's something that you want to work-out as early-on as possible, so that Yoshi's Liver and Kidney health, as well as his nutritional health is as good as it can be...The most common reasons that pet birds/parrots die long before they should is due to a regular, daily diet that is too high in fat and sugar and too low in protein, vitamins, minerals, etc.